U.S. patent application number 15/050620 was filed with the patent office on 2016-08-25 for optical position-measuring device.
The applicant listed for this patent is DR. JOHANNES HEIDENHAIN GMBH. Invention is credited to Wolfgang Holzapfel.
Application Number | 20160245642 15/050620 |
Document ID | / |
Family ID | 55299395 |
Filed Date | 2016-08-25 |
United States Patent
Application |
20160245642 |
Kind Code |
A1 |
Holzapfel; Wolfgang |
August 25, 2016 |
Optical Position-Measuring Device
Abstract
An optical position-measuring device for detecting the position
of two objects movable relative to each other includes a measuring
standard that is joined to one of the two objects and has a
measuring graduation having a periodic arrangement of graduation
regions along at least a first graduation direction. The
position-measuring device also includes a scanning unit having a
plurality of optical elements, which is disposed in a manner
allowing movement relative to the measuring standard. Via the
arrangement and formation of the optical elements of the scanning
unit, a scanning beam path results in which partial beams of rays
reaching interference propagate in mirror symmetry in relation to a
plane of symmetry and either fall in V-shaped fashion on the
measuring standard and/or are reflected back in a V-shape by the
measuring standard. The plane of symmetry is tilted by a defined
tilt angle about an axis of rotation that is oriented parallel to
the surface of the measuring standard and extends in a direction
perpendicular to the first graduation direction.
Inventors: |
Holzapfel; Wolfgang; (Obing,
DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
DR. JOHANNES HEIDENHAIN GMBH |
Traunreut |
|
DE |
|
|
Family ID: |
55299395 |
Appl. No.: |
15/050620 |
Filed: |
February 23, 2016 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01B 11/14 20130101;
G01D 5/38 20130101 |
International
Class: |
G01B 11/14 20060101
G01B011/14 |
Foreign Application Data
Date |
Code |
Application Number |
Feb 23, 2015 |
DE |
10 2015 203 188.8 |
Claims
1. An optical position-measuring device for detecting the position
of two objects movable relative to each other, comprising: a
measuring standard joined to one of the two objects and including a
measuring graduation having a periodic arrangement of graduation
regions along at least a first graduation direction; and a scanning
unit including a plurality of optical elements and being movable
relative to the measuring standard, arrangement and formation of
the optical elements of the scanning unit adapted to produce a
scanning beam path in which partial beams of rays reaching
interference propagate in mirror symmetry in relation to a plane of
symmetry and either fall in V-shaped fashion on the measuring
standard and/or are reflected back in a V-shape by the measuring
standard; wherein the plane of symmetry is tilted by a defined tilt
angle about an axis of rotation oriented parallel to a surface of
the measuring standard and extends in a direction perpendicular to
the first graduation direction.
2. The optical position-measuring device according to claim 1,
wherein a graduation period of the measuring graduation and the
tilt angle are selected such that the scanning beam path in the
scanning unit is identical to the scanning beam path in an untilted
state, in which the plane of symmetry is oriented perpendicular to
the surface of the measuring standard.
3. The optical position-measuring device according to claim 1,
wherein the partial beams of rays reach interference that result
from non-symmetrical orders of diffraction at the measuring
graduation.
4. The optical position-measuring device according to claim 3,
wherein the partial beams of rays reach interference which result
from one of the following combinations of orders of diffraction at
the measuring graduation: +3.sup.rd/-1.sup.st order of diffraction;
+1.sup.st/0.sup.th order of diffraction; -3.sup.rd/+1.sup.st order
of diffraction; and -1.sup.st/0.sup.th order of diffraction.
5. The optical position-measuring device according to claim 3,
wherein the measuring graduation includes a reflection phase
grating optimized to a high diffraction efficiency of the orders of
diffraction used for the signal generation.
6. The optical position-measuring device according to claim 1,
wherein the scanning unit includes at least one scanning plate
having a plurality of optical elements, the scanning plate being
disposed perpendicular to the plane of symmetry.
7. The optical position-measuring device according to claim 1,
wherein a scanning plate disposed in the scanning unit is
transparent, two first and two second scanning gratings are located
on a side of the scanning plate facing the measuring standard, and
two reflectors are located on an opposite side of the scanning
plate, reflecting sides of the reflectors being oriented in a
direction of the measuring standard.
8. The optical position-measuring device according to claim 7,
wherein the scanning unit is configured such that a beam of rays
emitted by a light source: strikes the measuring graduation and is
split into two partial beams of rays that correspond to two
different orders of diffraction and are reflected back in a V-shape
to the scanning unit; in the scanning unit, the two reflected-back
partial beams of rays pass through the two first scanning gratings
in the direction of the two reflectors, and in so doing, undergo a
deflection effect oriented anti-parallel to the direction of
incidence, as well as only a focusing effect perpendicular to the
first graduation direction; the partial beams of rays thus
deflected and focused then in each case impinge on the reflectors,
and are reflected back in the direction of the measuring standard;
the two reflected-back partial beams of rays then pass through the
two second scanning gratings in the direction of the measuring
standard, and in so doing, undergo a deflection effect in the first
graduation direction as well as only a collimating effect
perpendicular to the first graduation direction, so that the two
partial beams of rays then propagate in a V-shape in the direction
of the measuring standard; where the superposed partial beams of
rays are diffracted once more and reflected back in the direction
of the scanning unit.
9. The optical position-measuring device according to claim 1,
wherein the scanning unit includes at least one splitting element,
two deflecting elements, two reflectors, and two lenses.
10. The optical position-measuring device according to claim 9,
wherein the scanning unit is configured such that a beam of rays
emitted by a light source: is split via the splitting element into
two partial beams of rays, which then propagate in a direction of
respective deflecting elements; the partial beams of rays are
deflected via the deflecting elements to propagate in a V-shape in
a direction of a first point of incidence on the measuring
graduation; at the first point of incidence on the measuring
graduation, the partial beams of rays in each case undergo a first
diffraction and V-shaped reflection back in a direction of the
lenses and reflectors in the scanning unit; the partial beams of
rays traverse the lenses a first time, are reflected back by the
reflectors in a V-shape in a direction of incidence and pass
through the lenses a second time; the partial beams of rays then
impinge on the measuring graduation at a second point of incidence,
and in each case undergo a second diffraction and a V-shaped
reflection back in a direction of the deflecting elements in the
scanning unit.
11. The optical position-measuring device according to claim 1,
wherein the scanning unit includes at least one transparent
scanning plate and a structured photodetector, first and second
scanning gratings being disposed on a side of the scanning plate
facing an incoming beam of rays.
12. The optical position-measuring device according to claim 11,
wherein the scanning unit is configured such that a beam of rays
emitted by a light source: passes unaffected through the scanning
plate and then strikes the measuring graduation, where it is split
into two partial beams of rays that correspond to two different
orders of diffraction and are reflected back in V-shaped fashion to
the scanning unit; in the scanning unit, the two reflected-back
partial beams of rays pass through one of the two respective
scanning gratings, and in so doing, undergo a deflection effect in
a direction of the plane of symmetry and then propagate in a
direction of the structured photodetector, where they come
interferingly to superposition.
13. The optical position-measuring device according to claim 11,
wherein a second, identically configured scanning unit is firmly
joined mechanically to the scanning unit, the two scanning units
being tilted by the same angular amount but in opposite directions
about assigned axes of rotation oriented parallel to one
another.
14. A measuring system, comprising: a measuring graduation formed
as a two-dimensional cross grating that includes periodic
arrangements of graduation regions along first and second
graduation directions; and three pairs of position-measuring
devices as recited in claim 13, first and second pairs of the
position-measuring devices being disposed parallel to the first
graduation direction, a third pair of the position-measuring
devices being disposed parallel to the second graduation direction.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present application claims priority to Application No.
10 2015 203 188.8, filed in the Federal Republic of Germany on Feb.
23, 2015, which is expressly incorporated herein in its entirety by
reference thereto.
FIELD OF THE INVENTION
[0002] The present invention relates to an optical
position-measuring device.
BACKGROUND INFORMATION
[0003] In conventional position-measuring devices for detecting the
position of two objects movable relative to each other, usually the
position of a scanning unit relative to a measuring standard having
a measuring graduation disposed on it is determined along the
graduation direction of the measuring standard, the graduation
direction corresponding to the measuring direction; in this case,
the scanning unit and the measuring standard are each joined to one
of the two movable objects. In conventional devices, the so-called
sensitivity vector of the position-measuring device, which denotes
the specific effective measuring direction, is usually oriented
parallel to the surface of the measuring standard.
[0004] In addition, certain conventional position-measuring devices
have a sensitivity vector oriented obliquely to the surface of a
measuring standard having a reflective measuring graduation. For
example, reference is made to European Published Patent Application
No. 1 762 828, which is expressly incorporated herein in its
entirety by reference thereto. In such a position-measuring device,
the inclined orientation of the sensitivity vector is ensured by an
asymmetrical formation of the interferential scanning beam path. In
correspondent scanning beam paths, an incoming beam of rays is
split into at least two partial beams of rays that are ultimately
brought to interfering superposition. With the aid of such
position-measuring devices, it is possible to acquire position
information with regard to a relative movement of the scanning unit
and measuring standard along a lateral measuring or shift direction
and along a vertical measuring or shift direction. That is, with
the aid of a position-measuring device of this type, position
changes are able to be detected along two translatory degrees of
freedom of movement. In such a position-measuring device, the path
lengths of the interfering partial beams of rays are usually equal
only at a nominal scanning distance between the scanning unit and
measuring standard. If the measuring standard or the scanning unit
is moved out of this nominal scanning distance, different path
lengths in the partial beams of rays reaching interference then
result. Consequently, a possible change in the wavelength of the
light source used influences the phase of the interfering partial
beams of rays, and therefore also the position information
ascertained. For that reason, the scanning optical systems of
position-measuring devices of this type are described as chromatic.
Therefore, the light source used in them must exhibit sufficient
coherence length and an extremely low phase jitter. In order to
ensure this, a complex stabilization of such a light source is
necessary, making it correspondingly costly.
SUMMARY
[0005] Example embodiments of the present invention provide an
optical position-measuring device that has an inclined sensitivity
vector and is insensitive to wavelength changes in the case of all
permissible scanning distances.
[0006] According to an example embodiment of the present invention,
an optical position-measuring device for detecting the position of
two objects movable relative to each other includes: [0007] a
measuring standard that is joined to one of the two objects and has
a measuring graduation having a periodic arrangement of graduation
regions along at least a first graduation direction, and [0008] a
scanning unit having a plurality of optical elements, which is
disposed in a manner allowing movement relative to the measuring
standard, the arrangement and formation of the optical elements of
the scanning unit resulting in a scanning beam path in which
partial beams of rays reaching interference propagate in mirror
symmetry in relation to a plane of symmetry and either fall in
V-shaped fashion on the measuring standard and/or are reflected
back in a V-shape by the measuring standard. The plane of symmetry
is tilted by a defined tilt angle about an axis of rotation that is
oriented parallel to the surface of the measuring standard and
extends in a direction perpendicular to the first graduation
direction.
[0009] Preferably, the graduation period of the measuring
graduation and the tilt angle are selected such that the scanning
beam path in the scanning unit is identical to the scanning beam
path in the untilted state, in which the plane of symmetry is
oriented perpendicular to the surface of the measuring
standard.
[0010] Partial beams of rays may reach interference that result
from non-symmetrical orders of diffraction at the measuring
graduation.
[0011] In this context, partial beams of rays are able to reach
interference that result from one of the following combinations of
orders of diffraction at the measuring graduation:
[0012] +3rd/-1st order of diffraction,
[0013] +1st/0th order of diffraction,
[0014] -3rd/+1st order of diffraction, and
[0015] -1st/0th order of diffraction
[0016] It is possible for the measuring graduation to take the form
of a reflection phase grating which is optimized to a high
diffraction efficiency of the orders of diffraction used for the
signal generation.
[0017] In addition, the scanning unit may include at least one
scanning plate having a plurality of optical elements, the scanning
plate being disposed perpendicular to the plane of symmetry.
[0018] It may further be provided that a scanning plate disposed in
the scanning unit is transparent, two first and two second scanning
gratings are located on its side facing the measuring standard, and
two reflectors are located on the side of the scanning plate
opposite that, the reflecting sides of the reflectors being
oriented in the direction of the measuring standard.
[0019] In this case, the scanning unit may be arranged such that a
beam of rays emitted by a light source: [0020] strikes the
measuring graduation, where it is split into two partial beams of
rays that correspond to two different orders of diffraction and are
reflected back in a V-shape to the scanning unit; [0021] in the
scanning unit, the two reflected-back partial beams of rays pass
through the two first scanning gratings in the direction of the two
reflectors, and in so doing, undergo a deflection effect oriented
anti-parallel to the direction of incidence, as well as only a
focusing effect perpendicular to the first graduation direction;
[0022] the partial beams of rays thus deflected and focused then in
each case impinge on the reflectors and are reflected back in the
direction of the measuring standard; [0023] the two reflected-back
partial beams of rays then pass through the two second scanning
gratings in the direction of the measuring standard, and in so
doing, undergo a deflection effect in the first graduation
direction as well as only a collimating effect perpendicular to the
first graduation direction, so that the two partial beams of rays
then propagate in V-shaped fashion in the direction of the
measuring standard; [0024] where the superposed partial beams of
rays are diffracted once more and reflected back in the direction
of the scanning unit.
[0025] The scanning unit may include at least one splitting
element, two deflecting elements, two reflectors, and two
lenses.
[0026] In this case, the scanning unit may be arranged such that a
beam of rays emitted by a light source: [0027] is split via the
splitting element into two partial beams of rays, each of which
then propagates in the direction of the deflecting elements; [0028]
the partial beams of rays are deflected via the deflecting
elements, so that they propagate in a V-shape in the direction of a
first point of incidence on the measuring graduation; [0029] at the
first point of incidence on the measuring graduation, the partial
beams of rays in each instance undergo a first diffraction and
V-shaped reflection back in the direction of the lenses and
reflectors in the scanning unit; [0030] the partial beams of rays
traverse the lenses a first time, are reflected back by the
reflectors in V-shaped fashion in the direction of incidence, and
pass through the lenses a second time; and [0031] the partial beams
of rays then impinge on the measuring graduation at a second point
of incidence and in each case undergo a second diffraction and a
V-shaped reflection back in the direction of the deflecting
elements in the scanning unit.
[0032] The scanning unit may include at least one transparent
scanning plate as well as a structured photodetector, first and
second scanning gratings being disposed on the side of the scanning
plate facing the incoming beam of rays.
[0033] In this case, the scanning unit may be arranged such that a
beam of rays emitted by a light source: [0034] passes unaffected
through the scanning plate and then strikes the measuring
graduation, where it is split into two partial beams of rays that
correspond to two different orders of diffraction and are reflected
back in V-shaped fashion to the scanning unit; and [0035] in the
scanning unit, the two reflected-back partial beams of rays pass
through one of the two respective scanning gratings, and in so
doing, undergo a deflection effect in the direction of the plane of
symmetry and then propagate in the direction of the structured
photodetector, where they come interferingly to superposition.
[0036] Moreover, it is possible for a second, identically formed
scanning unit to be firmly joined mechanically to the scanning
unit, the two scanning units being tilted by the same angular
amount but in opposite directions about assigned axes of rotation
oriented parallel to one another.
[0037] In this context, the measuring graduation may take the form
of a two-dimensional cross grating that includes periodic
arrangements of graduation regions along the first and second
graduation direction, and has three pairs of position-measuring
devices firmly joined mechanically to one another, two pairs being
disposed parallel to the first graduation direction and the third
pair being disposed parallel to the second graduation
direction.
[0038] The optical position-measuring device described herein
provides that in a large range of permissible scanning distances,
it is insensitive to fluctuations in the light wavelength used.
Correct position values always result, even in the event of
possible changes in the wavelength. Therefore, markedly less
complex and more favorable light sources may be used in the
position-measuring device.
[0039] In addition, it is also possible to use the scanning unit of
the position-measuring device for scanning in which the sensitivity
vector is oriented parallel to the surface of the measuring
standard; these are customary practical applications in which, for
example, a relative shift of the scanning unit and measuring
standard along a measuring direction is intended to be determined
metrologically. It is therefore no longer necessary to develop and
keep on hand different scanning units for different measuring
tasks.
[0040] Further features and aspects of example embodiments of the
present invention are described in more detail below with reference
to the appended Figures.
BRIEF DESCRIPTION OF THE DRAWINGS
[0041] FIGS. 1a to 1c are schematic cross-sectional views of the
scanning unit of an optical position-measuring device according to
an example embodiment of the present invention, which is used in a
position-measuring device that has a sensitivity vector parallel to
the surface of the measuring standard scanned.
[0042] FIGS. 2a to 2c are schematic cross-sectional views of an
optical position-measuring device according to an example
embodiment of the present invention with an inclined sensitivity
vector.
[0043] FIGS. 3a and 3b are schematic cross-sectional views of an
optical position-measuring device according to an example
embodiment of the present invention with an inclined sensitivity
vector.
[0044] FIGS. 4a and 4b are schematic cross-sectional views of an
optical position-measuring device according to an example
embodiment of the present invention with an inclined sensitivity
vector.
[0045] FIG. 5 is a schematic cross-sectional view of a variant of
the optical position-measuring device illustrated in FIGS. 4a and
4b.
[0046] FIG. 6 schematically illustrates a further variant of the
optical position-measuring device illustrated in FIGS. 4a and
4b.
DETAILED DESCRIPTION
[0047] Before a number of exemplary embodiments of the optical
position-measuring device are described in detail with reference to
the Figures, first of all, a few concepts in connection therewith
are explained below.
[0048] To that end, reference is made once again to scanning
optical systems of position-measuring devices in which the
sensitivity vector is oriented parallel to the surface of the
measuring standard during measuring operation. In such scanning
optical systems, a beam of rays emitted by a light source is
usually split into two partial beams of rays. The two partial beams
of rays are diffracted at the measuring graduation of the measuring
standard into different orders of diffraction, and are eventually
superposed and brought to interference. In this manner, scanning
signals phase-shifted relative to each other are able to be
generated, from which position values are formed by incremental
counting and interpolation. Some such scanning optical systems
produce partial beams of rays which, from the splitting-up to the
superposition, extend in mirror symmetry in relation to a plane of
symmetry. In this operating mode, the planes of symmetry of such
scanning beam paths are perpendicular to the surface of the
measuring standard, and therefore also perpendicular to the
graduation direction of the measuring graduation of the measuring
standard. In this connection, the graduation direction corresponds
to the grating vector of the measuring graduation, the grating
vector always being oriented perpendicular to the grating lines of
the measuring graduation; therefore, hereinafter, the terms
graduation direction and grating vector are used interchangeably.
Because of the mirror symmetry of the scanning beam path, equally
long propagation paths of the partial beams of rays result between
the splitting and the recombination. The scanning optical system is
thus achromatic, that is, the wavelength of the light source as
well as its spectral distribution have no influence on the phase
and the degree of modulation of the scanning signals generated.
[0049] Moreover, scanning optical systems in which the partial
beams of rays reaching interference propagate in mirror symmetry in
relation to a plane of symmetry may also be arranged such that what
is termed the neutral pivot point of the scanning lies on the
measuring standard. In this connection, that point in space about
which either the scanning unit or the measuring standard is able to
be tilted without the position value displayed being changed is
referred to as the neutral pivot point. In the event of a tilting
about the neutral pivot point, the propagation paths covered by the
two partial beams of rays between the splitting and recombination
remain equal. Scanning optical systems of this type having
specularly symmetric partial beams of rays and neutral pivot point
on the measuring standard are also referred to hereinafter as
symmetrical V-type scanning optical systems. This designation thus
defines all those scanning optical systems whose two partial beams
of rays reaching interference first of all propagate in mirror
symmetry in relation to a plane of symmetry, and secondly, fall in
V-shaped fashion on one common scanning location on the measuring
standard and/or are reflected back in a V-shape from the scanning
location by the measuring standard. In this context, only the
points of incidence of both partial beams of rays on the measuring
standard along the graduation direction or along the grating vector
must be nearly identical; a displacement perpendicular to the
grating vector or along the longitudinal direction of the line-like
graduation regions is unimportant.
[0050] In addition to such scanning optical systems having
identical or nearly identical points of incidence of the two
partial beams of rays on the measuring standard along the grating
vector, there are further symmetrical scanning optical systems
whose neutral pivot point lies on the measuring standard. European
Published Patent Application No. 2 848 899, which is expressly
incorporated herein in its entirety by reference thereto, includes
a general description of the connection between an arbitrary beam
path of a scanning optical system and the associated position of
the neutral pivot point. Based on this description, further
scanning optical systems having a symmetrical beam path may be
indicated, whose neutral pivot point lies on the measuring
standard. All these scanning optical systems are also denoted
hereinafter as symmetrical V-type scanning optical systems.
[0051] During operation of such a symmetrical V-type scanning
optical system with a sensitivity vector parallel to the
measuring-standard surface, the scanning unit is aligned with
respect to the measuring standard having graduation period d.sub.M
such that the plane of symmetry mentioned above is perpendicular to
the surface of the measuring standard and also perpendicular to the
grating vector of the measuring graduation of the measuring
standard. This is called parallel alignment of scanning unit and
measuring standard.
[0052] An aspect of example embodiments of the present invention is
to tilt such a symmetrical V-type scanning optical system or the
associated plane of symmetry by a specific tilt angle .alpha. about
an axis of rotation that is oriented parallel to the surface of the
measuring standard and extends in a direction perpendicular to the
grating vector of the measuring graduation of the measuring
standard, that is, parallel to the longitudinal-extension direction
of the graduation regions of the measuring graduation. Suitable
further measures ensure that the scanning beam path in terms of the
scanning unit is identical to the scanning beam path in the
untilted state. In addition to the selection of a suitable tilt
angle .alpha., the additional measures include the selection of an
appropriate graduation period of the measuring graduation as well
as a selection of suitable partial beams of rays reaching
interference, that result from non-symmetrical orders of
diffraction at the measuring graduation.
[0053] A more detailed description of this aspect is provided below
with reference to an optical position-measuring device according to
an example embodiment of the present invention.
First Exemplary Embodiment
[0054] FIGS. 1a to 1c show various views of the scanning beam path
of an optical position-measuring device having a symmetrical V-type
scanning optical system. Here, sensitivity vector {right arrow over
(e)} of this scanning optical system is oriented parallel to the
surface of the measuring standard and parallel to the grating
vector of the measuring graduation or a first graduation direction
x; what is meant hereinafter in connection with such an orientation
of sensitivity vector {right arrow over (e)} is also what is
referred to as an in-plane operation of the corresponding
position-measuring device. FIG. 1a shows a view of the course of
the beam in the xz-plane of beam of rays S.sub.IN incoming from a
light source up to reflectors 23.sub.A, 23.sub.B; in FIG. 1c, the
course of the beam is illustrated in the same plane from reflectors
23.sub.A, 23.sub.B up to emergent signal beam of rays S.sub.OUT
with the superposed partial beams of rays that are propagating in
the direction of a detector unit; FIG. 1b shows the complete
scanning beam path in the yz-plane.
[0055] The optical position-measuring device illustrated in these
figures includes a measuring standard 10 that extends along first
graduation direction x, as well as a scanning unit 20 that is
disposed in a manner allowing movement relative to measuring
standard 10 at least along first graduation direction x. Measuring
standard 10 and scanning unit 20 are each joined to objects not
shown in the figures, e.g., to machine components movable relative
to each other. With the aid of the scanning signals generated via
the position-measuring device, a downstream machine control is able
to control the spatial positioning of these machine components.
[0056] Measuring standard 10 includes a graduated-scale support 11,
on whose surface a measuring graduation 12 is disposed that
includes a periodic arrangement of line-like graduation regions
along a first grating vector or along a first graduation direction
x; the longitudinal-extension direction of the graduation regions
corresponds in the figures to the y-direction. In the present
exemplary embodiment, measuring graduation 12 takes the form of a
reflection phase grating having graduation period d.sub.M as well
as a phase deviation of 180.degree., and provides a periodic
arrangement of graduation regions with different phase-shifting
effects for the light falling on them.
[0057] Of the various optical elements disposed in scanning unit
20, substantially only a transparent scanning plate 21, as well as
reflectors 23.sub.A, 23.sub.B located on its upper side and
scanning gratings 22.sub.A1, 22.sub.A2, 22.sub.B1, 22.sub.B2
situated on its lower side are shown in the figures. Not shown, on
the other hand, are the light source as well as the detector unit,
which, in principle, may likewise be located in scanning unit 20.
As an alternative, however, it is also possible to place these
elements apart spatially from scanning unit 20 and to connect them
to scanning unit 20 with the aid of optical fibers, via which
incoming beam of rays S.sub.IN and emergent signal beam of rays
S.sub.OUT, respectively, are then transmitted.
[0058] As becomes apparent in the following based on the detailed
descriptions of the various scanning beam paths, in each case the
arrangement and formation of the various optical elements in
scanning unit 20 ensure that a scanning beam path results in which
partial beams of rays A, B reaching interference propagate in
mirror symmetry in relation to a plane of symmetry SE. In this
context, they either fall in V-shaped fashion on measuring standard
10 and/or are reflected back in a V-shape from measuring standard
10.
[0059] After passing through transparent scanning plate 21, beam of
rays S.sub.IN incoming from the light source impinges
perpendicularly at first point of incidence P.sub.M on measuring
graduation 12 of measuring standard 10. There, it is split into two
partial beams of rays A, B reflected back in V-shaped fashion to
scanning unit 20. In this case, incoming beam of rays S.sub.IN is
split into symmetrical orders of diffraction n.sub.A1=+1 and
n.sub.B1=-1, and therefore into the two partial beams of rays A, B,
which have identical diffraction or deflection angles
.beta..sub.A=.beta..sub.B compared to the direction of incidence of
incoming beam of rays S.sub.IN. In this connection, it holds true
that:
sin ( .beta. A ) = sin ( .beta. B ) = .lamda. d M ( equation 1 )
##EQU00001##
in which:
[0060] .beta..sub.A represents the deflection angle of partial beam
of rays A compared to the direction of incidence of the incoming
beam of rays;
[0061] .beta..sub.B represents the deflection angle of partial beam
of rays B compared to the direction of incidence of the incoming
beam of rays;
[0062] .lamda. represents the light wavelength; and
[0063] d.sub.M represents the graduation period of the measuring
graduation.
[0064] Split partial beams of rays A and B then propagate to first
scanning gratings 22.sub.A1 and 22.sub.B1, respectively, on the
bottom side of transparent scanning plate 21 and pass through them.
In this instance, the two first scanning gratings 22.sub.A1 and
22.sub.B1 combine several optical functions in one common
diffractive structure. Thus, due to a deflection effect oriented
anti-parallel to the direction of incidence, partial beams of rays
A, B in the xz-projection (FIG. 1a) are again in each case directed
parallel to the optical axis in the z-direction. In the
yz-projection (FIG. 1b), partial beams of rays A, B are focused by
a cylindrical-lens function onto reflectors 23.sub.A, 23.sub.B on
the upper side of scanning plate 21, a focusing effect resulting
only perpendicular to direction x of the grating vector of the
measuring graduation or along its graduation direction x. Partial
beams of rays A, B thus deflected and focused then strike one
reflector 23.sub.A, 23.sub.B each, and are reflected there back in
the direction of measuring standard 10. After being reflected at
reflectors 23.sub.A, 23.sub.B, the two partial beams of rays A, B
pass through the two second scanning gratings 22.sub.A2, 22.sub.B2,
which likewise are disposed on the bottom side of scanning plate
21. The two second scanning gratings 22.sub.A2, 22.sub.B2 combine
functions corresponding to the two first scanning gratings
22.sub.A1, 22.sub.B1. Thus, they re-collimate partial beams of rays
A, B again by a cylindrical-lens function in the yz-projection
(FIG. 1b), and direct them in the xz-projection (FIG. 1c) back
again to one common point of incidence P.sub.M' on measuring
standard 10, i.e., on measuring graduation 12. In this context, the
two partial beams of rays A, B propagate in V-shaped fashion in the
direction of measuring standard 10, that is, in the direction of a
second point of incidence P.sub.M'. There, they are superposed by
diffraction again in symmetrical orders of diffraction n.sub.A2=+1
and n.sub.B2=-1 and brought to interference, and propagate in
signal beam of rays S.sub.OUT in the direction of scanning unit 20
and a detector unit, where a plurality of periodic, phase-shifted
scanning signals are obtained from signal beam of rays
S.sub.OUT.
[0065] As illustrated in FIGS. 1a, 1b, between splitting and
recombination, both partial beams of rays A, B extend in mirror
symmetry relative to a plane of symmetry SE, which here is
identical to the yz-plane from FIG. 1b, and in each case are
diffracted at the same points of incidence P.sub.M and P.sub.M',
respectively, of measuring graduation 12. Consequently, the neutral
pivot point of this scanning optical system lies on measuring
standard 10, that is, the scanning optical system is symmetrical
V-type. Partial beams of rays A, B reaching interference propagate
in mirror symmetry in relation to plane of symmetry SE, are first
of all reflected back in V-shaped fashion by measuring standard 10
and then fall in V-shaped fashion on measuring standard 10.
[0066] In the in-plane operation shown, signal period SP of the
periodic scanning signals generated with this position-measuring
device amounts to SP=d.sub.M/4. Sensitivity vector {right arrow
over (e)} is oriented parallel to the grating vector of measuring
graduation 12 extending in direction x.
[0067] In FIGS. 2a to 2c, an optical position-measuring device
according to an example embodiment of the present invention is
illustrated, which functions in what is referred to as out-of-plane
operation and, as illustrated in FIGS. 2a and 2c, has a sensitivity
vector {right arrow over (e)} that is inclined compared to the
surface of the measuring standard. Consequently, position-dependent
scanning signals are thus able to be generated both for the
relative movement of scanning unit and measuring standard along
first graduation direction x, i.e., along the grating vector of
measuring graduation 12 oriented in the x-direction, as well as
along direction z perpendicular to it. In this case, the
position-measuring device uses the same scanning optical system,
that is, the same scanning unit 20, as the position-measuring
device illustrated in FIGS. 1a to 1c. In contrast to that, here,
however, scanning unit 20, i.e., plane of symmetry SE--as
illustrated in FIGS. 2a and 21c--is tilted by a tilt angle .alpha.
about an axis of rotation in the y-direction; scanning plate 21
provided in scanning unit 20 is then also tilted correspondingly,
and therefore disposed perpendicular to plane of symmetry SE. The
corresponding axis of rotation is oriented parallel to the surface
of measuring standard 10' and extends in a direction perpendicular
to the grating vector of measuring graduation 12 oriented in the
x-direction. In addition, graduation period d.sub.M' of measuring
graduation 12' of the position-measuring device, where
d.sub.M'.noteq.d.sub.M, is selected differently from graduation
period d.sub.M of measuring graduation 12 of the position-measuring
device from FIGS. 1a to 1c explained above. Moreover, different
resulting orders of diffraction of measuring graduation 12' are
also used for the splitting and superposition of the two partial
beams of rays A, B than in the case of the conventional
position-measuring device illustrated in FIGS. 1a to 1c. With
regard to the traversal and impingement on the various optical
elements, the course of the scanning beam path corresponds to the
scanning beam path of the position-measuring device illustrated in
FIGS. 1a to 1c.
[0068] The differences, provided in addition to tilt angle .alpha.,
between the position-measuring device hereof and that illustrated
in FIGS. 1a to 1c are clarified in more detail in the following
description.
[0069] In the position-measuring device, partial beam of rays A is
diffracted twice in the +3.sup.rd order of diffraction at measuring
graduation 12' (n.sub.A1=n.sub.A2=+3), while partial beam of rays B
is deflected twice in the -1.sup.st order of diffraction
(n.sub.B1=n.sub.B2=-1). Tilt angle .alpha. and graduation period
d.sub.M' of measuring graduation 12' are selected such that, apart
from the tilting of plane of symmetry SE through tilt angle
.alpha., the beam path of the scanning optical system remains
identical to the beam path of the in-plane operation explained
above. That means that diffraction or deflection angles
.beta..sub.A' and .beta..sub.B' in the case of the diffraction at
measuring graduation 12' of the position-measuring device must be
identical to deflection angles .beta..sub.A=.beta..sub.B of the
position-measuring device in in-plane operation illustrated in
FIGS. 1a to 1c:
.beta.'.sub.A=.beta.'.sub.B=.beta..sub.A=.beta..sub.B (equation
2)
in which:
[0070] .beta.'.sub.A represents the deflection angle of partial
beam of rays A compared to the direction of incidence of the
incoming beam of rays in out-of-plane operation;
[0071] .beta.'.sub.B represents the deflection angle of partial
beam of rays B compared to the direction of incidence of the
incoming beam of rays in out-of-plane operation;
[0072] .beta..sub.A represents the deflection angle of partial beam
of rays A compared to the direction of incidence of the incoming
beam of rays in in-plane operation; and
[0073] .beta..sub.B represents the deflection angle of partial beam
of rays B compared to the direction of incidence of the incoming
beam of rays in in-plane operation.
[0074] Taking into account tilt angle .alpha., the following
deflection angles .beta..sub.A' and .beta..sub.B' result for the
diffraction at measuring graduation 12' with graduation period
d.sub.M' in orders of diffraction n.sub.A1 and n.sub.B1,
respectively:
- sin ( .alpha. ) + n A 1 .lamda. d M ' = sin ( .beta. A ' +
.alpha. ) ( equation 3 a ) - sin ( .alpha. ) + n B 1 .lamda. d M '
= sin ( - .beta. B ' + .alpha. ) ( equation 3 b ) ##EQU00002##
in which:
[0075] .alpha. represents the tilt angle;
[0076] n.sub.A1 represents the order of diffraction of partial beam
of rays A in the case of the first diffraction at the measuring
graduation;
[0077] n.sub.B1 represents the order of diffraction of partial beam
of rays B in the case of the first diffraction at the measuring
graduation;
[0078] .lamda. represents the light wavelength;
[0079] d'.sub.M represents the graduation period of the measuring
graduation for out-of-plane operation;
[0080] .beta.'.sub.A represents the deflection angle of partial
beam of rays A compared to the direction of incidence of the
incoming beam of rays in out-of-plane operation; and
[0081] .beta.'.sub.B represents the deflection angle of partial
beam of rays B compared to the direction of incidence of the
incoming beam of rays in out-of-plane operation.
[0082] From equations 1, 2, 3a, and 3b, ultimately the following
conditions 4a, 4b are obtained for the position-measuring
device:
- sin ( .alpha. ) + n A 1 .lamda. d M ' = .lamda. d M cos ( .alpha.
) + 1 - ( .lamda. d M ) 2 sin ( .alpha. ) ( equation 4 a ) - sin (
.alpha. ) + n B 1 .lamda. d M ' = - .lamda. d M cos ( .alpha. ) + 1
- ( .lamda. d M ) 2 sin ( .alpha. ) ( equation 4 b )
##EQU00003##
in which:
[0083] .alpha. represents the tilt angle;
[0084] n.sub.A1 represents the order of diffraction of partial beam
of rays A in the case of the first diffraction at the measuring
graduation;
[0085] n.sub.B1 represents the order of diffraction of partial beam
of rays B in the case of the first diffraction at the measuring
graduation;
[0086] .lamda. represents the light wavelength;
[0087] d'.sub.M represents the graduation period of the measuring
graduation for out-of-plane operation; and
[0088] d.sub.M represents the graduation period of the measuring
graduation for in-plane operation.
[0089] Equations 4a, 4b may be solved in terms of tilt angle
.alpha. and graduation period d.sub.M' of the measuring
graduation:
d M ' = 1 2 ( n A 1 - n B 1 ) 2 d M 2 + ( n A 1 - n B 1 ) 2 .lamda.
2 1 + 1 - ( .lamda. d M ) 2 ( equation 5 a ) .alpha. = arctan ( n A
1 + n B 1 n A 1 - n B 1 .lamda. d M 1 + 1 - ( .lamda. d M ) 2 ) (
equation 5 b ) ##EQU00004##
in which:
[0090] d'.sub.M represents the graduation period of the measuring
graduation for out-of-plane operation;
[0091] .alpha. represents the tilt angle;
[0092] n.sub.A1 represents the order of diffraction of partial beam
of rays A in the case of the first diffraction at the measuring
graduation;
[0093] n.sub.B1 represents the order of diffraction of partial beam
of rays B in the case of the first diffraction at the measuring
graduation;
[0094] .lamda. represents the light wavelength; and
[0095] d.sub.M represents the graduation period of the measuring
graduation for in-plane operation.
[0096] For each asymmetrical pair n.sub.A1, n.sub.B1
(n.sub.A.noteq.-n.sub.B) of orders of diffraction, equations 5a, 5b
supply an associated tilt angle .alpha.#0 and a graduation period
d.sub.M'.noteq.d.sub.M, via which it is ensured that the scanning
beam path extends symmetrically in relation to plane of symmetry
SE. Plane of symmetry SE remains unchanged relative to scanning
unit 20, and relative to measuring standard 10', is disposed tilted
by tilt angle .alpha. about an axis of rotation parallel to
measuring standard 10' and perpendicular to direction x of the
grating vector or the first graduation direction. The path lengths
of the two partial beams of rays A, B therefore remain equal, and
the scanning optical system--as called for--is also achromatic in
out-of-plane operation with inclined sensitivity vector {right
arrow over (e)}. That means that the same achromatic scanning
optical system or scanning unit 20 may be used both in the familiar
in-plane operation and in the out-of-plane operation. Consequently,
a double usage of corresponding scanning unit 20 is possible, and
the costly arrangement of a scanning optical system optimized
specifically for out-of-plane operation is no longer necessary. For
example, this simplifies the logistics considerably for a machine
manufacturer who wants to use both operating modes.
[0097] Equations 5a, 5b for symmetrical orders of diffraction
n.sub.A=-n.sub.B supply the trivial solutions .alpha.=0 and
d.sub.M'=d.sub.M of the in-plane operation of the device
illustrated in FIGS. 1a to 1c.
[0098] In the case of the resultant diffraction at measuring
graduation 12', other combinations of orders of diffraction may
also be used for the out-of-plane operation, so long as the
combinations are non-symmetrical according to the condition
n.sub.A1=n.sub.A2.noteq.-n.sub.B1=-n.sub.B2. In addition to the
combination with n.sub.A1=n.sub.A2=+3 and n.sub.B1=n.sub.B2=-1
described above, the combination of non-symmetrical orders of
diffraction with n.sub.A1=n.sub.A2=+1 and n.sub.B1=n.sub.B2=0 is
also especially favorable. In principle, however, other
non-symmetrical combinations of orders of diffraction are also
possible, for example, the combinations n.sub.A1=n.sub.A2=-3 and
n.sub.B1=n.sub.B2=+1 or n.sub.A1=n.sub.A2=+1 and
n.sub.B1=n.sub.B2=0, etc. For the out-of-plane operation, measuring
graduation 12' should be optimized to a high diffraction efficiency
of the orders of diffraction used for the signal generation.
[0099] In out-of-plane operation, sensitivity vector {right arrow
over (e)} is inclined by tilt angle .alpha. relative to the surface
of the measuring standard and to the grating vector of measuring
graduation 12' extending in the x-direction, and has the same
length as in in-plane operation. That means that signal period
SP.sub.x' of the scanning signals generated for a shift of the
measuring standard along the x-direction and signal period
SP.sub.z' of the scanning signals generated for a shift of the
measuring standard in the z-direction are given by the following
equations:
SP x ' = SP cos ( .alpha. ) ( equation 6 a ) SP z ' = SP sin (
.alpha. ) ( equation 6 b ) ##EQU00005##
in which:
[0100] SP.sub.x' represents the signal period of the scanning
signals generated for a shift of the measuring standard along the
x-direction;
[0101] SP.sub.z' represents the signal period of the scanning
signals generated for a shift of the measuring standard in the
z-direction;
[0102] SP represents the signal period of the same scanning optical
system in in-plane operation; and
[0103] .alpha. represents the tilt angle.
[0104] Exemplary values of a first exemplary embodiment of the
optical position-measuring device having a light wavelength
.lamda.=780 nm and a graduation period d.sub.M=2 .mu.m
(in-plane-operation) are summarized in the following Table 1:
TABLE-US-00001 TABLE 1 Operating mode n.sub.A1 = n.sub.A2 n.sub.B1
= n.sub.B2 .alpha. d.sub.M` SP.sub.X` SP.sub.Z` in-plane +1 -1
0.degree. -- (SP = 0.5 .mu.m) -- out-of-plane +3 -1 5.3729.degree.
4.0365 .mu.m 0.5022 .mu.m 5.3398 .mu.m out-of-plane +1 0
10.6529.degree. 1.0360 .mu.m 0.5088 .mu.m 2.7048 .mu.m
Second Exemplary Embodiment
[0105] FIGS. 3a and 3b illustrate the scanning optical system of a
second exemplary embodiment of the optical position-measuring
device in out-of-plane operation, that is, in operation with
inclined sensitivity vector {right arrow over (e)}. Analogous to
the depiction of the first exemplary embodiment, FIG. 3a
illustrates the course of the beam from light source 121 up to
reflectors 126.sub.A, 126.sub.B in the xz-plane, and FIG. 3b
illustrates the course of the beam in the xz-plane from reflectors
126.sub.A, 126.sub.E to detectors 128.1 to 128.3 of a detector
unit.
[0106] The entire scanning optical system, i.e., scanning unit 120
and thus plane of symmetry SE, is again tilted by a tilt angle
.alpha. about an axis of rotation. The axis of rotation is oriented
as in the preceding exemplary embodiment, namely, parallel to
measuring standard 110' and perpendicular to the grating vector of
measuring graduation 112' extending in the x-direction.
Consequently, in FIGS. 3a, 3b, the axis of rotation is
perpendicular to the drawing plane. A reflection phase grating with
180.degree. phase deviation is likewise provided again as measuring
graduation 112'.
[0107] The beam of rays emitted by light source 121, e.g., a laser
diode, is collimated with the aid of a collimating optical system
122 and split by a beam splitter 123 into two partial beams of rays
A, B. After being deflected by deflecting elements 124.sub.A,
124.sub.B, the two partial beams of rays A, B propagate in V-shaped
fashion in the direction of one common point of incidence P.sub.M
on measuring graduation 112' of measuring standard 110'. There,
they are diffracted in +3.sup.rd order (partial beam of rays A;
n.sub.A1=+3) and -1.sup.st order (partial beam of rays B;
n.sub.B1=-1) in reflection and are reflected in a V-shape back in
the direction of scanning unit 120. In scanning unit 120, partial
beams of rays A, B then traverse lenses 125.sub.A, 125.sub.B a
first time and subsequently strike reflectors 126.sub.A, 126.sub.B,
which are located in the focal planes of lenses 125.sub.A,
125.sub.B. From reflectors 126.sub.A, 126.sub.B, the partial beams
of rays are reflected back in V-shaped fashion in the direction of
incidence and then pass a second time through lenses 125.sub.A,
125.sub.B. Via the combination of lenses 125.sub.A, 125.sub.E with
reflectors 126.sub.A, 126.sub.B, a retroreflection of partial beams
of rays A, B thus takes place in anti-parallel fashion back to one
common point of incidence P.sub.M' on measuring graduation 112'.
There, partial beams of rays A, B are diffracted again into the
+3.sup.rd order (partial beam of rays A; n.sub.A2=+3) and into the
-1.sup.st order (partial beam of rays B; n.sub.B2=-1),
respectively, and then propagate via deflecting elements 124.sub.A,
124.sub.B back to beam splitter 123, which superposes both partial
beams of rays A, B to form one signal beam of rays. In each case,
further three beam splitters 127.1, 127.2, 127.3 subsequently
direct the signal beam of rays having the superposed partial beams
of rays to detectors 128.1, 128.2, 128.3 of a detector unit, which
generate a plurality of periodic, phase-shifted scanning
signals.
[0108] The phase shift of, e.g., 120.degree. necessary between the
scanning signals is achieved by additional polarization-optical
components that are not shown in FIGS. 3a and 3b. To that end,
prior to being superposed in beam splitter 123, the two partial
beams of rays A, B are polarized orthogonally relative to each
other. For that purpose, for example, .lamda./4 plates may be
inserted into the beam path of respective partial beams of rays A,
B, which they in each case traverse twice. In addition, mounted
directly in front of detectors 128.1, 128.2, 128.3 are polarizers
whose orientation determines the phase position of the associated
scanning signals, so that the desired phase position is thereby
able to be adjusted.
[0109] Analogous to the previous exemplary embodiment of the
position-measuring device, tilt angle .alpha. of scanning unit 120
or of plane of symmetry SE and graduation period d.sub.M' of
measuring graduation 112' on measuring standard 110' are selected
in defined manner in the present second exemplary embodiment, as
well. This is provided such that in out-of-plane operation, the
same beam path relative to tilted scanning unit 120 results as in
the case of in-plane operation of such a scanning unit 120, when
plane of symmetry SE is oriented perpendicular to the surface of
measuring standard 110'.
[0110] In this context, the following equation holds true in the
case of the in-plane operation of a scanning unit 120 according to
the second exemplary embodiment for deflection angles
.beta..sub.A1=.beta..sub.B1 and .beta..sub.A2=.beta..sub.B2 of
partial beams of rays A and B, analogous to equation 1 above:
- sin ( .beta. A 1 ) + .lamda. d M = sin ( .beta. A 2 ) ( equation
7 ) ##EQU00006##
in which:
[0111] .beta..sub.A1 represents the deflection angle of partial
beam of rays A falling on the measuring graduation compared to the
plane of symmetry in in-plane operation;
[0112] .beta..sub.A2 represents the deflection angle of partial
beam of rays A diffracted by the measuring graduation compared to
the plane of symmetry in in-plane operation;
[0113] .lamda. represents the light wavelength; and
[0114] d.sub.M represents the graduation period of the measuring
graduation for in-plane operation.
[0115] Analogous to equation 2 above, the following must hold true
for the present exemplary embodiment:
.beta.'.sub.A1=.beta.'.sub.B1=.beta..sub.A1=.beta..sub.B1 (equation
8a)
.beta.'.sub.A2=.beta.'.sub.B2=.beta..sub.A2=.beta..sub.B2 (equation
8b)
in which:
[0116] .beta..sub.A1 represents the deflection angle of partial
beam of rays A falling on the measuring graduation compared to the
plane of symmetry in in-plane operation;
[0117] .beta..sub.A2 represents the deflection angle of partial
beam of rays A diffracted by the measuring graduation compared to
the plane of symmetry in in-plane operation;
[0118] .beta..sub.B1 represents the deflection angle of partial
beam of rays B falling on the measuring graduation compared to the
plane of symmetry in in-plane operation;
[0119] .beta..sub.B2 represents the deflection angle of partial
beam of rays B diffracted by the measuring graduation compared to
the plane of symmetry in in-plane operation;
[0120] .beta.'.sub.A1 represents the deflection angle of partial
beam of rays A falling on the measuring graduation compared to the
plane of symmetry in out-of-plane operation;
[0121] .beta.'.sub.A2 represents the deflection angle of partial
beam of rays A diffracted by the measuring graduation compared to
the plane of symmetry in out-of-plane operation;
[0122] .beta.'.sub.B1 represents the deflection angle of partial
beam of rays B falling on the measuring graduation compared to the
plane of symmetry in out-of-plane operation; and
[0123] .beta.'.sub.B2 represents the deflection angle of partial
beam of rays B diffracted by the measuring graduation compared to
the plane of symmetry in out-of-plane operation.
[0124] The diffraction at measuring graduation 112' is described by
the following equations 9a, 9b:
- sin ( .beta. A 1 ' + .alpha. ) + n A 1 .lamda. d M ' = sin (
.beta. A 2 ' + .alpha. ) ( equation 9 a ) - sin ( - .beta. B 1 ' +
.alpha. ) + n B 1 .lamda. d M ' = sin ( - .beta. B 2 ' + .alpha. )
( equation 9 b ) ##EQU00007##
in which:
[0125] .beta.'.sub.A1 represents the deflection angle of partial
beam of rays A falling on the measuring graduation compared to the
plane of symmetry in out-of-plane operation;
[0126] .beta.'.sub.A2 represents the deflection angle of partial
beam of rays A diffracted by the measuring graduation compared to
the plane of symmetry in out-of-plane operation;
[0127] .beta.'.sub.A1 represents the deflection angle of partial
beam of rays B falling on the measuring graduation compared to the
plane of symmetry in out-of-plane operation;
[0128] .beta.'.sub.B2 represents the deflection angle of partial
beam of rays B diffracted by the measuring graduation compared to
the plane of symmetry in out-of-plane operation;
[0129] .alpha. represents the tilt angle;
[0130] n.sub.A1 represents the order of diffraction of partial beam
of rays A in the case of the first diffraction at the measuring
graduation in out-of-plane operation;
[0131] n.sub.B1 represents the order of diffraction of partial beam
of rays B in the case of the first diffraction at the measuring
graduation in out-of-plane operation;
[0132] .lamda. represents the light wavelength; and
[0133] d'.sub.M represents the graduation period of the measuring
graduation in out-of-plane operation.
[0134] Equations 7a, 7b, 8a, 8b, 9a, 9b may be combined in the
following manner:
- sin ( .alpha. ) cos ( .beta. A 1 ) - 1 - sin ( .alpha. ) 2 sin (
.beta. A 1 ) + n A 1 .lamda. d M ' = ( - sin ( .beta. A 1 ) +
.lamda. d M ) cos ( .alpha. ) + 1 - ( - sin ( .beta. A 1 ) +
.lamda. d M ) 2 sin ( .alpha. ) ( equation 10 a ) - sin ( .alpha. )
cos ( .beta. A 1 ) + 1 - sin ( .alpha. ) 2 sin ( .beta. A 1 ) + n B
1 .lamda. d M ' = - ( - sin ( .beta. A 1 ) + .lamda. d M ) cos (
.alpha. ) + 1 - ( - sin ( .beta. A 1 ) + .lamda. d M ) 2 sin (
.alpha. ) ( equation 10 b ) ##EQU00008##
in which:
[0135] .beta..sub.A1 represents the deflection angle of partial
beam of rays A falling on the measuring graduation compared to the
plane of symmetry in in-plane operation;
[0136] .alpha. represents the tilt angle;
[0137] n.sub.A1 represents the order of diffraction of partial beam
of rays A in the case of the first diffraction at the measuring
graduation in out-of-plane operation;
[0138] n.sub.B1 represents the order of diffraction of partial beam
of rays B in the case of the first diffraction at the measuring
graduation in out-of-plane operation;
[0139] .lamda. represents the light wavelength; and
[0140] d'.sub.M represents the graduation period of the measuring
graduation in out-of-plane operation.
[0141] Equations 10a, 10b may be solved in terms of tilt angle
.alpha. and graduation period d.sub.M' of measuring graduation 112'
for out-of-plane operation in the following manner:
d M ' = 1 2 ( n A 1 - n B 1 ) 2 d M 2 + ( n A 1 + n B 1 ) 2 .lamda.
2 cos ( .beta. A 1 ) + 1 - ( sin ( .beta. A 1 ) - .lamda. d M ) 2 (
equation 11 a ) .alpha. = arctan ( n A 1 + n B 1 n A 1 - n B 1
.lamda. d M cos ( .beta. A 1 ) + 1 - ( sin ( .beta. A 1 ) - .lamda.
d M ) 2 ) ( equation 11 b ) ##EQU00009##
in which:
[0142] .beta..sub.A1 represents the deflection angle of partial
beam of rays A falling on the measuring graduation compared to the
plane of symmetry in in-plane operation;
[0143] .alpha. represents the tilt angle;
[0144] n.sub.A1 represents the order of diffraction of partial beam
of rays A in the case of the first diffraction at the measuring
graduation in out-of-plane operation;
[0145] n.sub.B1 represents the order of diffraction of partial beam
of rays B in the case of the first diffraction at the measuring
graduation in out-of-plane operation;
[0146] .lamda. represents the light wavelength; and
[0147] d'.sub.M represents the graduation period of the measuring
graduation in out-of-plane operation.
[0148] Tilt angle .alpha. and graduation period d.sub.M' of
measuring graduation 112', determined according to equations 11a,
11b, ensure that the course of partial beams of rays A, B is also
symmetrical in out-of-plane operation, with plane of symmetry SE
again remaining unchanged relative to scanning unit 120. The path
lengths of the two partial beams of rays A, B remain equal. The
sign of tilt angle .alpha. may be reversed by permuting the values
of n.sub.A1 and n.sub.B1, at the same time, the value of graduation
period d.sub.M' of measuring graduation 112' remaining the same.
Thus, a scanning unit 120 is able to be used in both tilt positions
+.alpha. and -.alpha. in conjunction with the same measuring
standard 110'.
[0149] Incidentally, equations 11a and 11b represent a
generalization of equations 5a and 5b, and in the case of
.beta..sub.A1=0, are identical to them.
[0150] Different, non-symmetrical combinations of orders of
diffraction for the diffraction at measuring graduation 112' may be
used for the out-of-plane operation in this exemplary embodiment,
as well.
[0151] In out-of-plane operation, sensitivity vector {right arrow
over (e)}' is again inclined by angle .alpha. relative to the
surface of the measuring standard and has the same length as in
in-plane operation. That means that signal period SP.sub.x' for a
shift of the measuring standard along the x-direction and signal
period SP.sub.y' for a shift of the measuring standard in the
z-direction are again given by equations 6a and 6b.
[0152] Exemplary values for the second exemplary embodiment, with a
light wavelength .lamda.=780 nm, an angle of incidence
.beta..sub.A1=.beta..sub.B1=30.degree. and a graduation period
d.sub.M=1 .mu.m of the measuring graduation in in-plane operation,
are combined in the following Table 2.
TABLE-US-00002 TABLE 2 Operating mode n.sub.A1 = n.sub.A2 n.sub.B1
= n.sub.B2 .alpha. d.sub.M` SP.sub.X` SP.sub.Z` .beta..sub.A2 =
.beta..sub.B2 in-plane +1 -1 0.degree. -- (SP = 0.25 .mu.m) --
16.26.degree. out-of-plane +3 -1 11.573.degree. 2.0783 .mu.m 0.1552
.mu.m 1.2462 .mu.m 16.26.degree. out-of-plane +1 0 22.272.degree.
0.5743 .mu.m 0.2702 .mu.m 0.6596 .mu.m 16.26.degree.
[0153] From equations 8a, 8b, 9a and 9b, it is also possible to
derive tilt angle .alpha. and graduation period d.sub.M' in the
out-of-plane operation from predetermined deflection angles
.beta.'.sub.A1 and .beta.'.sub.A2, respectively, of partial beam of
rays A falling on measuring graduation 112' and diffracted by
measuring graduation 112' compared to plane of symmetry SE without
reference to parameters in the in-plane operation:
d M ' = .lamda. 2 n A 1 2 + n B 1 2 - 2 n A 1 n B 1 cos ( .beta. A
1 ' + .beta. A 2 ' ) cos ( ( .beta. A 1 ' - .beta. A 2 ' ) 2 ) (
sin ( .beta. A 1 ' + .beta. A 2 ' ) ) ( equation 11 c ) .alpha. =
.+-. arccos ( ( n A 1 - n B 1 ) ( cos ( .beta. A 1 ' ) + cos (
.beta. A 2 ' ) ) 2 cos ( .beta. A 1 ' - .beta. A 2 ' 2 ) n A 1 2 +
n B 1 2 - 2 n A 1 n B 1 cos ( .beta. A 1 ' + .beta. A 2 ' ) ) (
equation 11 d ) ##EQU00010##
in which:
[0154] .beta.'.sub.A1 represents the deflection angle of partial
beam of rays A falling on the measuring graduation compared to
plane of symmetry SE in out-of-plane operation;
[0155] .beta.'.sub.A2 represents the deflection angle of partial
beam of rays A diffracted by the measuring graduation compared to
plane of symmetry SE in out-of-plane operation;
[0156] .alpha. represents the tilt angle;
[0157] n.sub.A1 represents the order of diffraction of partial beam
of rays A in the case of the first diffraction at the measuring
graduation in out-of-plane operation;
[0158] n.sub.B1 represents the order of diffraction of partial beam
of rays B in the case of the first diffraction at the measuring
graduation in out-of-plane operation;
[0159] .lamda. represents the light wavelength; and
[0160] d'.sub.M represents the graduation period of the measuring
graduation in out-of-plane operation.
Third Exemplary Embodiment
[0161] The scanning optical system of a third exemplary embodiment
of the optical position-measuring device is illustrated in FIGS.
4a, 4b in out-of-plane operation, e.g., again in operation with
inclined sensitivity vector {right arrow over (e)}. FIG. 4a
illustrates the complete course of the beam in the scanning beam
path in the xz-plane, FIG. 4b illustrates the course of the beam in
the yz-plane.
[0162] The scanning optical system, i.e., scanning unit 220 and
thus plane of symmetry SE, is tilted by a tilt angle .alpha. about
an axis of rotation here, as well, the axis of rotation being
oriented as in the previous exemplary embodiments. Like in the
first example, scanning plate 223 is again disposed perpendicularly
in relation to plane of symmetry SE. A reflection phase grating is
provided as measuring graduation 212'. The grating vector of
measuring graduation 212', i.e., the first graduation direction, is
again oriented parallel to the x-direction.
[0163] The beam of rays emitted by a light source 221, e.g., taking
the form of a laser diode, is collimated by a collimating optical
system 222 and directed to measuring graduation 212' of a measuring
standard 210'. In this case, the beam of rays passes undeviated
through transparent scanning plate 223. Measuring graduation 212'
splits the incident beam of rays into the +3.sup.rd order of
diffraction (partial beam of rays A; n.sub.A1=+3) and into the
-1.sup.st order of diffraction (partial beam of rays B;
n.sub.B1=-1), that is, into partial beams of rays A and B,
respectively, that are reflected back in a V-shape in the direction
of scanning unit 220. In scanning unit 220, partial beams of rays
A, B then traverse one scanning grating 224.sub.A, 224.sub.B each.
In the present exemplary embodiment, both scanning gratings
224.sub.A, 224.sub.B are located on the upper side of scanning
plate 223, which is oriented facing away from measuring standard
210'. At scanning gratings 224.sub.A, 224.sub.B, partial beams of
rays A, B undergo a diffraction in the -1.sup.st order and
+1.sup.st order, and thus are deflected in the direction of plane
of symmetry SE. Deflected partial beams of rays A, B then propagate
in the direction of a structured photodetector 225, where they are
superposed and interfere with each other. Due to the interference,
a stripe pattern is formed in the detection plane that is detected
by structured photodetector 225 and converted into a plurality of
periodic, phase-shifted scanning signals.
[0164] Tilt angle .alpha. and graduation period d.sub.M' of
measuring graduation 212' are selected according to equations 5a,
5b above in this exemplary embodiment, as well. The course of the
beam is again symmetrical in relation to plane of symmetry SE,
which together with scanning unit 220, is tilted by tilt angle
.alpha. about an axis of rotation in the y-direction. Sensitivity
vector {right arrow over (e)} is also inclined by tilt angle
.alpha.. Equations 6a, 6b furnish signal periods SP.sub.x, SP.sub.z
for a shift of the measuring standard in the x-direction and
z-direction for this exemplary embodiment, as well.
[0165] Besides the use of the +3.sup.rd and -1.sup.st orders of
diffraction for partial beams of rays A, B, as an alternative, the
unsymmetrical orders of diffraction +1 and 0 could also be used at
measuring graduation 212' for producing partial beams of rays A, B
(n.sub.A1=+1, n.sub.B1=0), and so forth.
[0166] A first variant of the third example embodiment of the
optical position-measuring device is illustrated in FIG. 5. It
shows a position-measuring device having two scanning units 320.1,
320.2 according to the third exemplary embodiment explained above.
Both scanning units 320.1, 320.2 are joined firmly to each other
mechanically and are used for the optical scanning of one single or
common measuring standard 310'. First scanning unit 320.1 is tilted
by tilt angle +.alpha. about a first axis of rotation in the
y-direction; on the other hand, second scanning unit 320.2 is
tilted by tilt angle -.alpha. about a second axis of rotation,
likewise oriented in the y-direction, which is oriented parallel to
the first axis of rotation. Associated sensitivity vectors {right
arrow over (e)}.sub.1 and {right arrow over (e)}.sub.2,
respectively, are inclined symmetrically with respect to the
grating vector of measuring graduation 312' extending in the
x-direction. In both scanning units 320.1, 320.2, the arrangement
and scanning beam path correspond in each case to the third
exemplary embodiment described above.
[0167] In this variant, scanning units 320.1, 320.2 supply position
phases .PHI..sub.1 and .PHI..sub.2, respectively, on the output
side, that are obtained according to the following equations 12a,
12b:
.PHI. 1 = 2 .pi. SP X ' .DELTA. x M - 2 .pi. SP Z ' .DELTA. z M (
equation 12 a ) .PHI. 2 = 2 .pi. SP X ' .DELTA. x M - 2 .pi. SP Z '
.DELTA. z M ( equation 12 b ) ##EQU00011##
in which:
[0168] .PHI..sub.1 represents the position phase of the first
scanning unit;
[0169] .PHI..sub.2 represents the position phase of the second
scanning unit;
[0170] SP.sub.x' represents the signal period of the scanning
signals generated for a shift of the measuring standard along the
x-direction;
[0171] SP.sub.z' represents the signal period of the scanning
signals generated for a shift of the measuring standard in the
z-direction;
[0172] .DELTA.x.sub.M represents the shift of the measuring
standard in the x-direction; and
[0173] .DELTA.z.sub.M represents the shift of the measuring
standard in the z-direction.
[0174] By addition and subtraction of position phases .PHI..sub.1
and .PHI..sub.2 of the two scanning units 320.1, 320.2, z-position
.xi..sub.Z and x-position .xi..sub.X of the two scanning units
320.1, 320.2 relative to measuring standard 310' are able to be
determined independently:
.xi. X = SP X ' 4 .pi. ( .PHI. 1 + .PHI. 2 ) ( equation 13 a ) .xi.
Z = SP Z ' 4 .pi. ( .PHI. 2 - .PHI. 1 ) ( equation 13 b )
##EQU00012##
in which:
[0175] .xi..sub.x represents the x-position of the two scanning
units relative to the measuring standard;
[0176] .xi..sub.Z represents the z-position of the two scanning
units relative to the measuring standard;
[0177] .PHI..sub.1 represents the position phase of the first
scanning unit;
[0178] .PHI..sub.2 represents the position phase of the second
scanning unit;
[0179] SP.sub.X' represents the signal period of the scanning
signals generated for a shift of the measuring standard along the
x-direction; and
[0180] SP.sub.z' represents the signal period of the scanning
signals generated for a shift of the measuring standard in the
z-direction.
[0181] A second variant of the third example embodiment of the
optical position-measuring device is illustrated in FIG. 6. It
illustrates a measuring system which includes three pairs of
scanning units 420.1 to 420.6 on the scanning side according to the
variant illustrated in FIG. 5. With the aid of the three pairs of
scanning units 420.1 to 420.6, a measuring graduation 412' on
measuring standard 410' is scanned, which is in the form of a
two-dimensional cross grating and therefore has two collinear
grating vectors and thus a first and second graduation direction,
which in FIG. 6, are oriented parallel to the x-direction and
y-direction. In this case, all six scanning units 420.1 to 420.6
are joined rigidly to each other.
[0182] The pairs of scanning units 420.1/420.2, 420.3/420.4 and
420.5/420.6, as in FIG. 5, are in each case tilted in opposite
direction by tilt angle .alpha.. Scanning-unit pairs 420.1/420.2
and 420.3/420.4 are in each instance sensitive with regard to
relative movements in the x-direction and z-direction;
scanning-unit pair 420.5/420.6 is sensitive with regard to relative
movements in the y-direction and z-direction. Each pair of scanning
units 420.1/420.2, 420.3/420.4, 420.5/420.6 allows determination of
the z-position of the cross-grating measuring graduation relative
to scanning units 420.1 to 420.6. In this context, the effective
measuring locations for measuring the z-position in each case lie
in the middle between the scanning units of each pair. Thus, the
z-position of measuring standard 410' is determined at three
different and non-collinear locations. In addition, each of the
first two scanning-unit pairs 420.1/420.2 and 420.3/420.4 supplies
an x-position of measuring standard 410' whose measuring location
is different in the y-direction and allows determination of the
tilting Rz of measuring standard 410' about the z-axis.
Furthermore, scanning-unit pair 420.5/420.6 supplies the y-position
of measuring standard 410'. With this arrangement of scanning units
420.1 to 420.6, it is therefore possible to determine the position
of measuring standard 410' in all six degrees of freedom x, y, z,
Rx, Ry, Rz. It is also possible to determine only a portion of the
degrees of freedom using a correspondingly smaller number of
scanning units.
* * * * *